Problems with hard cutting videos when using different frame rates and speed control
I strongly suspect this is a bit of a duplicate question, even though it isn't terribly clear to a cursory examination. That is, I have a hunch that your image and / or video is compressed using a relatively highly compressed codec. When this happens, especially with long Group Of Pictures codecs (long GOP), you can expect that your hard cuts will not be able to be maintained because you will likely have cut in the middle of one of these GOP runs. When this happens, your video is unable to properly sync because the precise frame cut position has happened in a place that is unrecoverable, and as a result the codec decoder must resume from the previous "whole" frame.

While this might not be apparent immediately, similar sorts of issues crop up with heavily compressed audio and the result is very similar.

So how to resolve this? Convert your entire stream or streams to a native image format or AVI JPG series, and audio to WAV format.

Why does this solve the issue? Because then, wherever you place a cut, the image and audio have an immediate ability to be resumed at wherever the cut point ends up, without requiring a "rewinding", which is causing the issue.

While I am not 100% certain, I would wager that there is a greater than 50% chance this is your issue. If it turns out to be the case, there are other folks that are vastly more capable at finding the duplicates and citing them here.